{"id":7754,"date":"2021-11-06T00:42:32","date_gmt":"2021-11-05T19:12:32","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7754"},"modified":"2021-11-06T01:35:57","modified_gmt":"2021-11-05T20:05:57","slug":"what-is-the-integration-of-sin-inverse-x-whole-square","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-integration-of-sin-inverse-x-whole-square\/","title":{"rendered":"What is the integration of sin inverse x whole square ?"},"content":{"rendered":"

Solution :<\/h2>\n

We have, I = \\((sin^{-1}x)^2\\) dx<\/p>\n

Let \\(sin^{-1}x\\) = t, Then, x = sin t \\(\\implies\\) dx = cos t dt<\/p>\n

\\(\\therefore\\) I = \\(\\int\\) \\((sin^{-1}x)^2\\) dx<\/p>\n

I = \\(\\int\\) \\(t^2\\) cos t dt<\/p>\n

Applying integration by parts and,<\/p>\n

Taking \\(t^2\\) as first function and cos t as second function,<\/p>\n

I = \\(t^2\\) (sin t) – \\(\\int\\) (sin t) – \\(\\int\\) 2t sin t dt = \\(t^2\\) sin t – 2 \\(\\int\\) t sin t dt<\/p>\n

Again applying integration by parts and,<\/p>\n

Taking t as first function and sin t as second function,<\/p>\n

I = \\(t^2\\) sin t – 2{ t ( -cos t) – \\(\\int\\) 1 \\(\\times\\) (-cos t) dt }<\/p>\n

I = \\(t^2\\) sin t – 2{ -t cos t + \\(\\int\\) cos t dt }<\/p>\n

I = \\(t^2\\) sin t – 2( -t cos t + sin t ) + C<\/p>\n

I = \\(t^2\\) sin t – 2{ -t \\(\\sqrt{1 – sin^2 t}\\) + sin t } + C<\/p>\n

I = \\(xsin^{-1} x\\) – 2{ – \\(\\sqrt{1 – x^2} sin^{-1}x\\) + x } + C<\/p>\n

\n

Similar Questions<\/h3>\n

What is the integration of sin inverse root x ?<\/a><\/p>\n

What is integration of sin inverse cos x ?<\/a><\/p>\n

What is the integration of x sin inverse x dx ?<\/a><\/p>\n

What is the integration of tan inverse root x ?<\/a><\/p>\n

What is the integration of x tan inverse x dx ?<\/a><\/p>\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : We have, I = \\((sin^{-1}x)^2\\) dx Let \\(sin^{-1}x\\) = t, Then, x = sin t \\(\\implies\\) dx = cos t dt \\(\\therefore\\) I = \\(\\int\\) \\((sin^{-1}x)^2\\) dx I = \\(\\int\\) \\(t^2\\) cos t dt Applying integration by parts and, Taking \\(t^2\\) as first function and cos t as second function, I = \\(t^2\\) …<\/p>\n

What is the integration of sin inverse x whole square ?<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[52,43],"tags":[],"yoast_head":"\nWhat is the integration of sin inverse x whole square ? - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the integration of sin inverse x whole square by using integration by parts.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/what-is-the-integration-of-sin-inverse-x-whole-square\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is the integration of sin inverse x whole square ? 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